A parametric interatomic potential is constructed for graphene. The potential energy consists of two parts: bond energy and radial interaction energy. The bond energy part is a generalized version of the Tersoff-Brenner potential. It includes angular terms and explicitly accounts for flexural deformation of the lattice normal to the plane of graphene. The range of interaction of each atom extends up to its fourth neighbor atoms in contrast to the Tersoff-Brenner potential that extends to only up to second neighbors. The parameters of the potential are obtained by fitting the calculated values to the cohesive energy, lattice constant, elastic constants, and the phonon frequencies of graphene. The values of the force constants between an atom and other atoms that are within its fourth neighbor distance are calculated. The flexural rigidity of the graphene lattice is calculated in terms of the force constants and is found to be 2.12 eV, which is much higher than 0.797 eV calculated earlier using the Tersoff-Brenner potential.
Physical Review B (Condensed Matter and Materials Physics)